I think that the best way to start this writing process would be to outline your ideas, during the process you should list the reasons that qualify you to be the leader and maybe what the downside would be if you couldn't be the leader. In your speech you can use the list of the downside to strengthen your argument, leaving the listeners with no room for doubt. If you include a rough draft here, it would be a little easier to help with the direction of the speech. I hope this helps!

Yes, the need for a ruler in any area that has a sizable population is self-evident, and need not concern you. If you were really entering into politics, I'd suggest you focus on outlining not only your own qualifications but on demonizing your opponent, too. Dig up some dirt on him/her, and if you can't find any, invent some. But, since this is a school assignment, I suppose you should settle for explaining your vision of the island under your leadership.

That's odd. I would have pegged you as the sort of person who believed in public education, public health care, environmental regulation, etc., all of which need government bureaucracies to administer to them, a body of lawmakers to regulate them, etc. For that matter, even when I was at my most strictly libertarian, I still acknowledged that a society at least needs a police force and a military if it is to maintain its integrity, and these in turn need the oversight of ruling body (preferably one accountable to an electorate). A small tribe might be able to get away with doing everything by consensus, acting as one big committee (though in practice the smartest and most able, or possibly just the strongest, would end up becoming a defacto chief even then), but with millions of people, all of the things I've mentioned require the coordination of rulers, though they might call themselves administrators or managers to be more PC.

I was questioning the singular -- a ruler, which implies a single person ruling over everybody else, rather than people making decisions collectively, perhaps through their representatives in government or perhaps in some other way.

Ah. I was thinking of the representatives as rulers, most likely headed by a single person who can coordinate them the way they coordinate others -- much the way every nation in the world has at present.

Right: That's where democracy often goes wrong, when the representatives of the people start to think of themselves as rulers rather than representatives. It's even worse for the person tapped to fill the central coordinating position, whatever that might be called. Representative democracy seems to work well at the local level, where people see and really are accountable to those they represent, but the representatives becomes more and more ruler-like as the size of the government body in question grows. However, I do seem to see a reversal of the trend in the EU these days. Something about each country being only one of a collective, the rules of which must be followed by all, seems to have an inhibiting effect on the hubris of national leaders.